Is a person sinful for placing a "Donate to Me" icon on a personal blog to request financial assistance to complete university studies, knowing that the donor is unknown (whether Muslim or Christian) and fearing that their money might come from an unlawful source?

What you have done falls under "begging," which is permissible for only three types of individuals: one who has taken on a debt (diyah or indemnity), one who has been afflicted by a disaster, or one who has been struck by poverty, as testified by his people. If you are among those for whom begging is permissible, then there is no harm in collecting donations until your need is met, even if the donor is a disbeliever or if his money is unlawfully gained, based on the statement of Sheikh al-Islam Ibn Taymiyyah: "The default assumption regarding what is in the possession of a Muslim is that it is his property." However, if you are not among those for whom begging is permissible, then you must cease what you have been doing.